fix(g4): close fixture-top pose_tolerance via iterated fixed-point converged-rest; flag bimodal cabinet

[KE7]

Summary

Closes the g4 NON-CONVERGENT FIXTURE-TOP residual (RCA g4_remaining_arenas.md §3b). Task objects resting on a fixture exterior top never reach a stable rest inside the 50-step validation settle, so no single analytic clearance is a fixed point and they fail g4 pose_tolerance on z. This PR implements a principled iterated fixed-point (converged-rest) measurement and emits the converged z (Option-2: renderer z == settled z; gate stays 5 mm). Zero band-aid: no tolerance widening, no masking, no exclusion.

Non-convergence diagnosis

The analytic on-fixture spawn z (spawn_clearance rule 2) uses the fixture AABB top (highest geom), which sits far above the real rest face:

• flat_stove cook_region is a visual-only grate (same mode as fix(distractor-settle): identity rest-orient for bowl_drainer + measured stability gate for tall distractors on the flat_stove grate #32/feat(fixtures): seat alphabet_soup on flat_stove burner plate (un-exclude from grate) #34)
• microwave / cabinet tops have a raised lip / rounded shell

So the object is injected too high and falls ~48–64 mm per 50-step settle — a constant per-injection drop (no fixed point at 50 steps), exactly matching the predecessor's observation. This is diagnosis (a) (over-estimated rest face), not (b) (rolls/oscillates).

Fixed-point method

scripts/measure_g4_fixture_fixedpoint.py iterates the settle map f(z) = settle50(inject at z) from the analytic z until |Δz| < 1 mm — the object has landed on its true rest face and the 50-step map is now a fixed point. Roll-off guard: if xy drifts >30 mm (slid off) the case is flagged, not recorded. The harness auto-discovers every :init fixture-supported object from the realized scene's support_surface_class (robust to init-vs-goal grep confusion). A corpus :init-block scan confirms these are the only 3 task-object-on-fixture-exterior pairs in the whole BDDL set.

Both recorded objects fall straight down (xy drift <0.15 mm — not a roll-off) to a deterministic converged rest.

Per-case before/after (position subset, real LIBERO env, 3 seeds)

pair	converged z*	clearance	BEFORE	AFTER	dz before→after
white_bowl|microwave	0.8994	0.0794	0/9 fail	9/9 pass	48.8 → 0.0 mm
akita_black_bowl|flat_stove	0.8984	0.0784	0/6 fail	6/6 pass	64.5 → 1.2 mm

Determinism: spread ≤ 1.5 mm across 6 seeds × all :init tasks/instances.

Flagged residual (not forced)

akita_black_bowl|wooden_cabinet — the cabinet top has a non-uniform collision surface: a solid edge region rests at z*≈1.126 (clear 0.306), visual-gap regions fall to ≈0.898 (clear 0.078), and the top_drawer placement is genuinely metastable across seeds (0.898↔1.119, spread 221 mm). No single scalar is a fixed point across the sampled xy region; forcing the dominant 0.078 would inject the solid-region bowl inside the cabinet body (contact-explosion regression risk). Per the no-force guard it is FLAGGED — it needs an xy-aware rest surface (out of scope for scalar Option-2).

Additive-merge evidence

• spawn_clearances_variants.json: +2 rows, 0 changed, 0 removed (proven by semantic diff) + a provenance _meta block.
• Untouched: fixture_geometry.json, stack_offsets.json, spawn_clearances.json, asset_metadata.py, consistency.py (5 mm gate) — all byte-identical.
• The two new rows resolve via the existing rule 1 of spawn_clearance, superseding the rule-2 analytic for these two pairs only; every other pair (renderer + simulator) is byte-identical.

No-regression control

Untouched arenas (STUDY + table-center, all classes, position+object, 3 seeds): 30/30 = 100% pass, max dz 1.98 mm. white_bowl|table byte-identical (proves the microwave row is isolated). All wooden_cabinet cases fail identically before/after (flagged, unchanged).

Tests / CI

• CI Tier-1 (test_scenic, test_perturbation_policy, test_sweep_g3_budget, test_invariants_*): 182 passed
• Validation smoke (G0–G3 on 2-task × 3-subset sweep): 6/6 pass
• test_spawn_z_consistency: 102 passed (updated test_fixture_task_residual → asserts measured pairs present at fixed-point value + cabinet stays flagged)
• ruff + ruff-format + black clean on src/ + tests/

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